// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
#include "sparse.h"
#include <Eigen/SparseQR>

template<typename MatrixType, typename DenseMat>
int
generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150)
{
	eigen_assert(maxRows >= maxCols);
	typedef typename MatrixType::Scalar Scalar;
	int rows = internal::random<int>(1, maxRows);
	int cols = internal::random<int>(1, maxCols);
	double density = (std::max)(8. / (rows * cols), 0.01);

	A.resize(rows, cols);
	dA.resize(rows, cols);
	initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
	A.makeCompressed();
	int nop = internal::random<int>(0, internal::random<double>(0, 1) > 0.5 ? cols / 2 : 0);
	for (int k = 0; k < nop; ++k) {
		int j0 = internal::random<int>(0, cols - 1);
		int j1 = internal::random<int>(0, cols - 1);
		Scalar s = internal::random<Scalar>();
		A.col(j0) = s * A.col(j1);
		dA.col(j0) = s * dA.col(j1);
	}

	//   if(rows<cols) {
	//     A.conservativeResize(cols,cols);
	//     dA.conservativeResize(cols,cols);
	//     dA.bottomRows(cols-rows).setZero();
	//   }

	return rows;
}

template<typename Scalar>
void
test_sparseqr_scalar()
{
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef SparseMatrix<Scalar, ColMajor> MatrixType;
	typedef Matrix<Scalar, Dynamic, Dynamic> DenseMat;
	typedef Matrix<Scalar, Dynamic, 1> DenseVector;
	MatrixType A;
	DenseMat dA;
	DenseVector refX, x, b;
	SparseQR<MatrixType, COLAMDOrdering<int>> solver;
	generate_sparse_rectangular_problem(A, dA);

	b = dA * DenseVector::Random(A.cols());
	solver.compute(A);

	// Q should be MxM
	VERIFY_IS_EQUAL(solver.matrixQ().rows(), A.rows());
	VERIFY_IS_EQUAL(solver.matrixQ().cols(), A.rows());

	// R should be MxN
	VERIFY_IS_EQUAL(solver.matrixR().rows(), A.rows());
	VERIFY_IS_EQUAL(solver.matrixR().cols(), A.cols());

	// Q and R can be multiplied
	DenseMat recoveredA = solver.matrixQ() * DenseMat(solver.matrixR().template triangularView<Upper>()) *
						  solver.colsPermutation().transpose();
	VERIFY_IS_EQUAL(recoveredA.rows(), A.rows());
	VERIFY_IS_EQUAL(recoveredA.cols(), A.cols());

	// and in the full rank case the original matrix is recovered
	if (solver.rank() == A.cols()) {
		VERIFY_IS_APPROX(A, recoveredA);
	}

	if (internal::random<float>(0, 1) > 0.5f)
		solver.factorize(A); // this checks that calling analyzePattern is not needed if the pattern do not change.
	if (solver.info() != Success) {
		std::cerr << "sparse QR factorization failed\n";
		exit(0);
		return;
	}
	x = solver.solve(b);
	if (solver.info() != Success) {
		std::cerr << "sparse QR factorization failed\n";
		exit(0);
		return;
	}

	// Compare with a dense QR solver
	ColPivHouseholderQR<DenseMat> dqr(dA);
	refX = dqr.solve(b);

	bool rank_deficient = A.cols() > A.rows() || dqr.rank() < A.cols();
	if (rank_deficient) {
		// rank deficient problem -> we might have to increase the threshold
		// to get a correct solution.
		RealScalar th =
			RealScalar(20) * dA.colwise().norm().maxCoeff() * (A.rows() + A.cols()) * NumTraits<RealScalar>::epsilon();
		for (Index k = 0; (k < 16) && !test_isApprox(A * x, b); ++k) {
			th *= RealScalar(10);
			solver.setPivotThreshold(th);
			solver.compute(A);
			x = solver.solve(b);
		}
	}

	VERIFY_IS_APPROX(A * x, b);

	// For rank deficient problem, the estimated rank might
	// be slightly off, so let's only raise a warning in such cases.
	if (rank_deficient)
		++g_test_level;
	VERIFY_IS_EQUAL(solver.rank(), dqr.rank());
	if (rank_deficient)
		--g_test_level;

	if (solver.rank() == A.cols()) // full rank
		VERIFY_IS_APPROX(x, refX);
	//   else
	//     VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );

	// Compute explicitly the matrix Q
	MatrixType Q, QtQ, idM;
	Q = solver.matrixQ();
	// Check  ||Q' * Q - I ||
	QtQ = Q * Q.adjoint();
	idM.resize(Q.rows(), Q.rows());
	idM.setIdentity();
	VERIFY(idM.isApprox(QtQ));

	// Q to dense
	DenseMat dQ;
	dQ = solver.matrixQ();
	VERIFY_IS_APPROX(Q, dQ);
}
EIGEN_DECLARE_TEST(sparseqr)
{
	for (int i = 0; i < g_repeat; ++i) {
		CALL_SUBTEST_1(test_sparseqr_scalar<double>());
		CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double>>());
	}
}
